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Physical Review Letters

Experimental Realization of High-Efficiency Counterfactual Computation

Fei Kong, Chenyong Ju, Pu Huang, Pengfei Wang, Xi Kong, Fazhan Shi, Liang Jiang, Jiangfeng Du

Published Aug 21, 2015• 21 citations
Publisher

Abstract

Counterfactual computation (CFC) exemplifies the fascinating quantum process by which the result of a computation may be learned without actually running the computer. In previous experimental studies, the counterfactual efficiency is limited to below 50%. Here we report an experimental realization of the generalized CFC protocol, in which the counterfactual efficiency can break the 50% limit and even approach unity in principle. The experiment is performed with the spins of a negatively charged nitrogen-vacancy color center in diamond. Taking advantage of the quantum Zeno effect, the computer can remain in the not-running subspace due to the frequent projection by the environment, while the computation result can be revealed by final detection. The counterfactual efficiency up to 85% has been demonstrated in our experiment, which opens the possibility of many exciting applications of CFC, such as high-efficiency quantum integration and imaging.

DOI
10.1103/physrevlett.115.080501

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Counterfactual computation (CFC) exemplifies the fascinating quantum process by which the result of a computation may be learned without actually running the computer. In previous experimental studies, the counterfactual efficiency is limited to below 50%. Here we report an experimental realization of the generalized CFC protocol, in which the counterfactual efficiency can break the 50% limit and even approach unity in principle. The experiment is performed with the spins of a negatively charged nitrogen-vacancy color center in diamond. Taking advantage of the quantum Zeno effect, the computer can remain in the not-running subspace due to the frequent projection by the environment, while the computation result can be revealed by final detection. The counterfactual efficiency up to 85% has been demonstrated in our experiment, which opens the possibility of many exciting applications of CFC, such as high-efficiency quantum integration and imaging.
Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer. Such processes are possible within quantum physics and to achieve this effect a computer embodying the possibility of running the computation must be available, even though the computation is, in fact, not run. We study the possibilities and limitations of protocols for the counterfactual computation of decision problems (where the result r is either 0 or 1). If p⊂r denotes the probability of learning the result r 'for free' in a protocol, then one might hope to design a protocol which simultaneously has large p⊂0 and p⊂1. However, we prove that p⊂0 + p⊂1 ≤ 1 in any protocol of this type and derive further constraints on p⊂0 and p⊂1 in terms of N, the number of times that the computer is not run. In particular, we show that any protocol with p⊂0 + p⊂1 = 1 – ∈ must have N tending to infinity as ∈ tends to 0. We show that ‘interaction–free’ measurements can be regarded as counterfactual computations, and our results then imply that N must be large if the probability of interaction is to be close to zero. Finally, we consider some ways in which our formulation of counterfactual computation can be generalized.
Raman-excited spin coherences were experimentally observed in nitrogen-vacancy (N-V) diamond color centers by means of nondegenerate four-wave mixing and electromagnetically induced transparency. The maximal absorption suppression was found to be 17%, which corresponds to 70% of what is possible given the random geometric orientation of the N-V center in diamond. In the context of quantum computing in solids, this level of transparency represents efficient preparation of quantum bits, as well as the ability to perform arbitrary single-quantum-bit rotations.
Already in 430 BC ancient Greek's philosopher Zeno of Elea formulated his well known paradox: An object that can be observed at any instant of time at a well defined position can not move. Today, this paradox is solved by the infinitesimal calculus invented by Newton and Leibniz in the 18 century. Nevertheless in 1977 it was shown that Zeno's paradox rises again from the formalism of quantum mechanics [1]. We present our latest measurement results on the quantum Zeno effect in a solid state spin, namely the ground state spin of a single negatively charged nitrogen vacancy (NV) center in diamond [2]. These results are supported by an extended theoretical analysis and give evidence that the quantum Zeno effect is physical reality not only in atomic systems [3], but also in nanoscopic solid state systems [4].
Nitrogen-vacancy (NV) centers in diamond are versatile candidates for many quantum information processing tasks, ranging from quantum imaging and sensing through to quantum communication and fault-tolerant quantum computers. Critical to almost every potential application is an efficient mechanism for the high fidelity readout of the state of the electronic and nuclear spins. Typically such readout has been achieved through an optically resonant fluorescence measurement, but the presence of decay through a meta-stable state will limit its efficiency to the order of 99%. While this is good enough for many applications, it is insufficient for large scale quantum networks and fault-tolerant computational tasks. Here we explore an alternative approach based on dipole induced transparency (state-dependent reflection) in an NV center cavity QED system, using the most recent knowledge of the NV center's parameters to determine its feasibility, including the decay channels through the meta-stable subspace and photon ionization. We find that single-shot measurements above fault-tolerant thresholds should be available in the strong coupling regime for a wide range of cavity-center cooperativities, using a majority voting approach utilizing single photon detection. Furthermore, extremely high fidelity measurements are possible using weak optical pulses.
ABSTRACT The quantum Zeno effect, which inhibits quantum state evolution via repeated weak measurements, significantly enhances the efficiency of interaction‐free measurement (IFM). This fundamental mechanism facilitates high‐efficiency counterfactual quantum communication, enabling information delivery without particle transmission through the channel. However, the transmission time of the counterfactual communication requires minutes for bit and suffers the bit error when transmitting an image. Applying the quantum Zeno effect, we experimentally demonstrate high‐efficiency weak‐trace‐free counterfactual communication on a quantum photonic chip, achieving a transmission probability of 74.2 1.6% for bit 0 and 85.1 1.3% for bit 1. Furthermore, we successfully transmit our group's logo – Quanta – through counterfactual communication, and reduce the time cost from minutes to seconds for bit, with zero bit errors after information processing. Our study provides a promising approach for secure and efficient communication using integrated silicon quantum photonics.